Лямбда-выражения в VB.NET должны иметь возвращаемое значение, решение - метод-оболочка.
Public Shared Function RenderPartialToString(ByVal userControl As String, ByVal viewData As Object, ByVal tempData As Object, ByVal controllerContext As ControllerContext) As String
Dim h As New HtmlHelper(New ViewContext(controllerContext, New WebFormView("omg"), viewData, tempData), New ViewPage())
Dim blockRenderer As New MvcContrib.UI.BlockRenderer(controllerContext.HttpContext)
Dim s = blockRenderer.Capture(New Action(Function() renderPartialLambda(h, userControl, viewData)))
Return s
End Function
Private Shared Function renderPartialLambda(ByVal html As HtmlHelper, ByVal userControl As String, ByVal viewData As Object)
RenderPartialExtensions.RenderPartial(html, userControl, viewData)
Return Nothing
End Function